On quasi Cauchy double sequences in metric spaces
Advanced Studies: Euro-Tbilisi Mathematical Journal, vol.19, no.2, pp.265-273, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 19 Issue: 2
- Publication Date: 2026
- Doi Number: 10.32513/asetmj/193220082619216
- Journal Name: Advanced Studies: Euro-Tbilisi Mathematical Journal
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.265-273
- Keywords: continuity, double sequences, P-convergent
- Istanbul University Affiliated: Yes
Abstract
A double sequence x ={xk,1} in a metric space ℕ is quasi-Cauchy if given an ε>0 there exists an N ϵ N such that d(xk,1,xk+1,l+1),d(xk,1,xk+1,l),d(xk,1,xk+1,l+1)<ε for k,l>N. We study continuity type properties of factorable double functions defined on a double subset E× E of X2 into X, and obtain interesting results related to compactness, uniform continuity, sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset E× E of X2 into X.